Find the volume of the solid generated by revolving the area bounded by x² - 2kx - 4ky + k² = 0 and 4x - 4y + k = 0 about the line x = -2k.
Find the volume of the solid generated by revolving the area bounded by x² - 2kx - 4ky + k² = 0 and 4x - 4y + k = 0 about the line x = -2k.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Show the graph and solve for intersection points
Transcribed Image Text:Find the volume of the solid generated by revolving the
area bounded by x² - 2kx - 4ky + k² = 0 and
4x - 4y + k = 0 about the line x = -2k.
![(Circular Disk):
Horizontal Axis of Rev.:
V = 1 [R(x)]² dx
Vertical Axis of Rev.:
V=If [R(y)]² dy
Horizontal Axis of Rev.:
Vertical Axis of Rev.:
V = 1
П
(Cylindrical Shell):
V:
1 = 211 frl dr
(Circular ring/Washer):
V = 1 {[R(x)]²[r(x)]²} dx
{[(y)]²[(y)]²} dy
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67e83fa8-cdbb-4376-b0a6-7f089ddc4414%2F3b313f39-574a-405b-b591-aee7b420a2c0%2F7vzdq6g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(Circular Disk):
Horizontal Axis of Rev.:
V = 1 [R(x)]² dx
Vertical Axis of Rev.:
V=If [R(y)]² dy
Horizontal Axis of Rev.:
Vertical Axis of Rev.:
V = 1
П
(Cylindrical Shell):
V:
1 = 211 frl dr
(Circular ring/Washer):
V = 1 {[R(x)]²[r(x)]²} dx
{[(y)]²[(y)]²} dy
-
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